From early days, I was interested in mathematics and used to scribble answers to mathematical puzzles on napkins (when we were in a restaurant) or on anything else I could find to write on. As a City College student I commuted two hours each way on the subway, from Brooklyn where I lived, to City College, and spent four hours a day doing mathematical puzzles and my course work on the trains. Some people might find that a puzzle by itself. But everything about the mind is a puzzle, and how the human race came to think in language and in numbers---especially in numbers---is perhaps life’s biggest puzzle.
That question--or puzzle--widened for me throughout my years of teaching, reading, doing research---and thinking. Eventually, I became interested in Piaget’s studies of how the child’s brain develops, and did my doctoral thesis on mathematical modeling of Piaget’s thesis. Epistemology---or the philosophy of thought--what it is and how we do it, and why some people can’t--or won’t do mathematics began to intrigue me. Problem-solving, it seemed to me, is the biggest game adults play, and we should all like to play it as much as we like to play golf or a computer game. Some brains are galvanized by problems, and other brains are paralyzed by them. The question led everywhere---into neurophysiological inquiry, philosophy, education, personal trauma, and the nature of mathematics and science.
One insight haunted me: there was a problem with how we were taught to regard learning, that the end was the big prize rather than the journey. In fact, students are taught to disregard the journey, which is often fraught with error. They are taught that error is shameful. This attitude has had an adverse impact on the sciences, when scientists have been taught not to disclose the errors by which they arrived at their insights Whereas error is one way to learn, error helps the brain evolve; error helps free us.
It is a revolutionary thought: there is no life without error, no thinking without error, and no science without error. The intellectual revolution is to understand the dynamical and fruitful interplay between knowing and erring.
From these ideas emerged my books on epistemology: The Persistence of Error, and Knowing and Erring
Bob addressing a meeting of the Piaget Society, Berkeley
|In time, another idea emerged as the basis for how the mind/brain works, and that is that it always works metaphorically. Metaphor, like error, is at the foundation of intellectual work. Metaphor is even the basis of “one plus one equals two.” (see paper on methapor under Articles, Stories, Essays). All is metaphor.
Error and metaphor are inescapable elements in the intellectual journey. My work is resonant with Piaget and Einstein because they recognized the role of imagination in thought.
The idea of the mind embodied in time and space as well as in the physical body, led me early on to some mystics. I became interested in some yoga practices---but I am not a mystic. I am wedded to the idea of the physiological in its intersection and interaction with time and space---which is also why I am not a Platonist. Plato’s metaphor, in the famous passage of the cave, of the mind’s interaction with knowledge posits a passive learner in the shadow of reality . The learner sees, “as in a glass darkly,” to quote St. Paul’s famous statement, and then one day the shadows disappear. At the heart of my epistemological journey is a dynamic learner who constructs the world in his mind/brain in a dynamic and epistemological tension with reality. Responses to my ideas are welcome. Just hit contact and remember to give me your name and email address, thank you.